Re: Sixth normal form

On 7 aug, 20:36, vldm10 <vld..._at_yahoo.com> wrote:
> On Aug 1, 7:36 am, Jan Hidders <hidd..._at_gmail.com> wrote:
>
> > Any attempt to reformulate it to something easier or more intuitive in
> > my experience almost always ends up with something that is either
> > wrong or actually harder to understand.
>
> > The only somewhat mysterious part may be the "JD is implied by the
> > CKs" but this can be tested by the following simple procedure:
>
> > 1. Let jd be the join dependency we want to test
> > 2. While jd has two elements (being sets of attributes) Si and Sj such
> > that the intersection of Si and Sj contains a candidate key do:
> > 2.1 replace Si and Sj with the union of Si and Sj
> > 3. If jd contains the header of the relation (which is also a set of
> > attributes) then return "yes" else "false"
> > -- Jan Hidders
>
> You gave here the procedure which is more on intuitive level than
> based on some formal system.

Although somewhat informally described by me, it is a proper algorithm
and as such *is* a formal system that has been proven both sound and
complete.

> Now we can set the question - why mentioned procedure for misterios
> part is combination of formal and intuitive. Although, mentioned
> procedure is useful, I beleive it is good to be aware of the
> following:
>
> a) Cks are based on FDs and for FDs there is a formal system.
> b) For JDs there is no formal system in the sense of complete
> inference rules.

JDs have been succesfully axiomatized. In fact, much larger classes
including MVDs, FDs and much more have been axiomatized. See the Alice
book for a wealth of information on that.